11. Container With Most Water (Medium)

Source:https://leetcode.com/problems/container-with-most-water/
Time:2020/12/20

Description
Given n non-negative integers a1, a2, …, an , where each represents a point at coordinate (i, ai). n vertical lines are drawn such that the two endpoints of the line i is at (i, ai) and (i, 0). Find two lines, which, together with the x-axis forms a container, such that the container contains the most water.

Notice that you may not slant the container.

Example 1:

Input: height = [1,8,6,2,5,4,8,3,7]
Output: 49
Explanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.
Example 2:

Input: height = [1,1]
Output: 1
Example 3:

Input: height = [4,3,2,1,4]
Output: 16
Example 4:

Input: height = [1,2,1]
Output: 2

Constraints:

n = height.length
2 <= n <= 3 * 104
0 <= height[i] <= 3 * 104

Solution
Approach1: Bruce force

class Solution {
    
    
    public int maxArea(int[] height) {
    
    
        int res = -1;
        
        for(int i = 0; i < height.length; i++)
            for(int j = i; j < height.length; j++)
            {
    
    
                int h = Math.min(height[i], height[j]);
                int a = j - i;
                res = Math.max(res, a * h);
            }
        
        return res;
    }
}

Approach 2: Two Pointer Approach
But moving the shorter line’s pointer could turn out to be beneficial, as per the same argument, despite the reduction in the width.

class Solution {
    
    
    public int maxArea(int[] height) {
    
    
        int res = -1;
        int l = 0, r = height.length - 1;
        
        while(l < r)
        {
    
    
            res = Math.max((r- l) * Math.min(height[l], height[r]), res);
            if(height[l] < height[r])
                l++;
            else
                r--;
        }
        
        return res;
    }
}